The present invention concerns a process of cyclic detection in diversity of polarization of digital cyclostationary radioelectric signals. Notably, the invention concerns the detection of such radioelectric signals by two antennas of radiation diagram sensitive to orthogonal polarization of the signals. The invention is applicable in the field of radiocommunications.
In the field of radiocommunications, the utilization of digital signals is rapidly increasing. During a radio communication a transmitter emits radioelectric signals in one or more frequency channels each characterized by a frequency bandwidth Bmax and a central frequency. The signals transmitted in these frequency channels are characterized by a number of parameters such as the binary bit rate, the modulation index and the carrier frequency. Appendix A contains a glossary of terms used in the text. There are known techniques for calculating the spectral correlation or the cyclic correlation of cyclostationary signals to determine these parameters and detect these signals. Appendix B contains some definitions and properties concerning cyclostationary signals, 2nd order cyclic statistics and the spectral correlation of such signals. Known systems implementing these techniques perform this detection using a signal received on a single antenna. Notably, the known FAM algorithm (meaning Fast Fourier Transform Accumulation Method) has been the object of numerous publications, in particular those of the colloquium xe2x80x9c4th ASSP Workshop on spectrum modeling, August 1988xe2x80x9d, such as xe2x80x9cDigital implementation of spectral correlation analyzersxe2x80x9d by W. A. Brown, H. H. Loomis, and xe2x80x9cComputationally efficient algorithms for cyclic spectral analyzers"" by R. S. Roberts, W. A. Brown, H. H. Loomis. The FAM algorithm enables rapid calculation of the estimators of spectral correlation by means of FFT in the whole cyclic frequency/harmonic frequency (xcex1,f) space.
The estimator of the first moment E[x(fk)x(fm)*] is expressed as:                                                                         γ                ^                            x1                        ⁡                          (                                                α                  0                                ,                                  f                  0                                            )                                =                                    ∑                              t                =                1                            K                        ⁢                                          x                ⁡                                  (                                                            f                      k                                        ,                    t                                    )                                            ⁢                                                x                  ⁡                                      (                                                                  f                        m                                            ,                      t                                        )                                                  *                            ⁢              exp              ⁢                              {                                                      -                    j2πδα                                    ⁢                                      xe2x80x83                                    ⁢                  t                                }                                                    ⁢                  
                ⁢                  with          ⁢                      xe2x80x83                    ⁢                      f            0                          =                                                                              f                  k                                +                                  f                  m                                            2                        ⁢                          xe2x80x83                        ⁢            and            ⁢                          xe2x80x83                        ⁢                          α              0                                =                                    f              k                        -                          f              m                        +                          δ              ⁢                              xe2x80x83                            ⁢              α                                                          (        1        )            
The estimator of the second moment E[x(fk)x(xe2x88x92fm)] is expressed as:                                                                         γ                ^                            x2                        ⁡                          (                                                α                  0                                ,                                  f                  0                                            )                                =                                    ∑                              t                =                1                            K                        ⁢                                          x                ⁡                                  (                                                            f                      k                                        ,                    t                                    )                                            ⁢                              x                ⁡                                  (                                                            -                                              f                        m                                                              ,                    t                                    )                                            ⁢              exp              ⁢                              {                                                      -                    j2πδα                                    ⁢                                      xe2x80x83                                    ⁢                  t                                }                                                    ⁢                  
                ⁢                  with          ⁢                      xe2x80x83                    ⁢                      f            0                          =                                                                              f                  k                                -                                  f                  m                                            2                        ⁢                          xe2x80x83                        ⁢            and            ⁢                          xe2x80x83                        ⁢                          α              0                                =                                    f              k                        +                          f              m                        +            δα                                              (        2        )            
The signals x(f,t) are calculated by a bank of band filters Bcanal and central frequency filters denoted fk, fm. The signal x(f,t) therefore has a band equal to Bcanal. To obtain the exact frequency representation of the signal x(t), Bcanal must be very much smaller than the band B of the signal x(t). Since x(f) is calculated in a non-null band, this signal x(f) evolves with time and is therefore a function of f and t: x(f,t). In a first stage, the signals x(fk,t) and x(fm,t)* are intercorrelated after having been displaced to the base band. These signals being in a non-null band Bcanal, the signal z(t) obtained evolves with time in a band of width 2xc3x97Bcanal. Given that z(t) is in a non-null band and that the correlation peak in cyclic frequency does not necessarily lie in fk-fm, it is necessary to perform a Fourier transform of z(t) to obtain the offset xcex4xcex1 of this correlation peak.
To enable a rapid calculation of the estimators of spectral correlation, {circumflex over (xcex3)}x1 and {circumflex over (xcex3)}x2, the FAM algorithm is implemented in several stages.
In a first stage, the signals x(fk,t) and x(xe2x88x92fm,t) are calculated by a system of smooth FFTs. The difference xcex94xcex1=fk+1xe2x88x92fk between the frequencies fk+1 and fk is constant and the sampling frequency of the signals x(f,t) is             Fe      canal        =          Fe      RE        ,
where RE is the shift of the moving windows (expressed as a number of samples) and Fe is the sampling frequency of x(t).
In a second stage, the signal z(t)=x(fk,t)xc3x97x(fm,t)* is calculated for the first moment and the signal z(t)=x(fk,t)xc3x97x(xe2x88x92fm,t) is calculated for the second moment.
In a third stage, an FFT is performed on the signal z(t) on a number of samples.
On the first moment to calculate the spectral correlation in   f  =            (                        f          k                +                  f          m                    )        2  
and for xcex1 lying between xcex1min=fkxe2x88x92fmxe2x88x92{fraction (xcex1/2)} and xcex1max=fkxe2x88x92fm+xcex94{fraction (xcex1/2)} on K samples, an FFT of the signal z(t)=x(fk,t)xc3x97x(fm,t)* must be performed on K samples. The K frequency sales of the resulting signal z(xcex1k) represent the spectral correlation in   f  =            (                        f          k                +                  f          m                    )        2  
with xcex1k lying between       α    min    =            f      k        -          f      m        -                  Fe        canal            2      
and       α    max    =            f      k        -          f      m        +                            Fe          canal                2            .      
Since Fecanal is greater than xcex94xcex1, only the cyclic frequencies xcex1k contained in the interval (fkxe2x88x92fmxe2x88x92xcex94{fraction (xcex1/2)}) . . . (fkxe2x88x92fm+xcex94{fraction (xcex1/2)} are retained. All the outputs X(fk,t) and x(fm,t) of the bank of filters are correlated to obtain the points of the spectral correlation in the zone of interest of the first moment, in other words for xcex1 less than Bmax.
On the second moment, the calculation of the spectral correlation is limited in harmonic frequency by Bmax.
The FAM algorithm described previously is applicable only to signals from a single antenna. However, in the field of radiocommunications signals propagate with a degree of polarization and the gain of all antennas is dependent on the polarization of the signals received. This polarization dependence means that a single antenna filters the sources and can even completely cancel out the signals received, which would make detection of the sources impossible. This remark is true whatever algorithm is used, in particular a FAM algorithm.
The object of the invention is to propose a solution to this problem. For this purpose, the invention is a process of cyclic detection in diversity of polarization of digital cyclostationary radioelectric signals of sampling frequency Fe transmitted in a frequency channel of bandwidth Bmax and received on a network of N antennas, N being at least two, whose radiation diagram has a maximum maximorum of sensitivity wherein, for any pair of antennas, said process consists in acquiring over an observation period T and in an acquisition band Bacq the digital signals output by the antennas, in calculating, for each cyclic frequency of a determined cyclic frequency/harmonic frequency space limited by the bandwidth Bmax. of the frequency channel and the acquisition band Bacq of the digital signals acquired, a cyclic covariance matrix on a first moment of a spectral correlation of the digital signals acquired, and a cyclic covariance matrix on a second moment of a spectral correlation of the digital signals acquired, and in detecting peaks of spectral correlation by comparing a likelihood ratio determined from each said cyclic covariance matrix with a detection threshold determined statistically.
The invention consists in a cyclic detection test of radioelectric signals received by any pair of antennas of a network of N antennas whose radiation diagram presents a maximum maximorum (maximum of the maxima) of sensitivity.
In a first embodiment of the process, the network includes N=2 antennas whose maximums maximorum of sensitivity point in orthogonal directions.
In a second embodiment of the process, the network includes N=2 antennas whose maximums maximorum of sensitivity point in the same direction.
The main advantage of the invention is that it performs a rapid test of detection of radioelectric signals of arbitrary polarization by calculating a likelihood ratio using a simple relation. In the case of a network with two antennas and in the absence of a source, the likelihood ratio follows a statistical chi-square law with 8 degrees of freedom. The knowledge of the probability law of the likelihood ratio in the absence of a source enables a detection threshold to be calculated with a certain probability of false alarm to judge the presence of a source in a determined part of the cyclic frequency/harmonic frequency space.
The cyclic detection test of the likelihood ratio is based on two antennas and is also statistical. Consequently, the detection is not made using an empirical detection threshold.
The process according to the invention also provides the advantage of enabling the differentiation of radioelectric signals present in the same frequency channel but transmitted at different bit rates. The process according to the invention advantageously enables separation of radioelectric signals according to their modulation frequency and their transmission bit rate.